Exercise 30.1
Question 31
Find the vector equation of the plane passing through the points (2,5,-3), (-2,-3,5),(5,3,-3)
Sol :
Question 32
Can there be a unique equation of the plane passing through points (2,5,-3), (-2,-3,5) and (5,3,-3). Give reasons for your answer.
Sol :
TYPE-VI
Question 33
Find the coordinates of the point where the line $\frac{x+1}{2}=\frac{y+2}{3}=\frac{z+3}{4}$ meets the plane x+y+4z=6.
Sol :
Question 34
(i) Find the coordinates of the point where the line through $(3,-4,-5)$ and $(2,-3,1)$ crosses the plane 2x+y+z=7
(ii) Find the coordinates of the point where the line through the points A(3,4,1) and B(5,1,6) crosses the xy-plane.
(iii) Find the coordinates of the point where the line through (5,1,6) and (3,4,1) crosses the zx-plane.
Sol :
Question 35
Find the coordinates of the point where the line through (5,1,6) and (3,4,1) crosses the yz-plane.
Question 36
Find the distance of the point (-1,-5,-10) from the point of intersection of the line $\vec{r}=2 \hat{i}-\hat{j}+2 \hat{k}+\lambda(3 \hat{i}+4 \hat{j}+2 \hat{k})$ and the plane $\vec{r} \cdot(\hat{i}-\hat{j}+\hat{k})=5$
Sol :
Question 37
Find the coordinates of the foot of perpendicular drawn from origin to the planes
(i) x+y+z=1
(ii) 3y+4z-6=0
(iv) 2x+3y+4z-12=0
(v) 2x-3y+4z-6=0
(iii) 5y+8=0
Sol :
Question 38
(i) Find the image of the point (2,-3,4) with respect to the plane 4x+2y-4z+3=0.
(ii) Find the image of the point (1,3,4) in the plane 2x-y+z+3=0.
(iii) From the point P(1,2,4) a perpendicular in drawn on the plane 2x+y-2z+3=0. Find the equation, the length and the coordinates of the foot of perpendicular.
Sol :
TYPE-VII
Question 39
Find the equation of the plane passing through the intersection of the planes $\vec{r} \cdot(2 \hat{i}+\hat{j}+3 \hat{k})=7, \vec{r} \cdot(2 \hat{i}+5 \hat{j}+3 \hat{k})=9$ and the point (2,1,3)
Sol :
Question 40
Find the equation of the plane passing through the intersection of the planes $\vec{r} \cdot(2 \hat{i}+\hat{j}+3 \hat{k})=7, \vec{r} \cdot(2 \hat{i}+5 \hat{j}+3 \hat{k})=9$ and the point (3,2,-1).
Sol :
No comments:
Post a Comment